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Cork Institute of Technology
Bachelor of Engineering (Honours) in Structural Engineering-Award
(Bachelor of Engineering in Structural Engineering – Award)
(NFQ – Level 8)
Autumn 2005
Systems Analysis
(Time: 3 Hours)
Instructions Answer FOUR questions. All questions carry equal marks. Statistical Tables are provided.
Examiners: Mr. T. Corcoran Prof. P. O Donoghue Mr. D. O Hare
Section A
- (a) Use either the M-technique or the two-phase method to solve the following problem:
maximise subject to
z x x x x x x x x
1 2 1 2 1 2 1 ,^2. (b) Consider the problem: maximise subject to
z x x x x x x x x x x x x
1 2 3 1 2 3 1 2 3 1 ,^2 . (i) Write down the dual of the above problem. (ii) Solve the dual problem graphically. (iii) Deduce the optimum value of the primal objective function and, using the idea of complementary slackness, determine which primal variables are basic at the optimum solution.
- A manufacturing process involves two stages, A and B. There are 4500 spare man- machine hours available in stage A and 4000 spare man-machine hours available in stage B. Four products are to be considered for manufacture and the relevant time requirements are shown below:
Time requirement, in hours, per 100 units Product 1 2 3 4 Stage A 10 30 80 40 Stage B 20 10 10 30 The profit levels for the products, per unit, are €10, €10, €40, and €30, respectively. (a) Formulate the above problem as a linear programming problem where the objective is to maximise total financial return. Find the optimal solution using the simplex method, and state clearly what this solution is. (b) The marketing department considers the solution to be unreasonable. They think that at most 5000 units of product 4 could be sold at that level of profit. In order to sell 10000 units, they believe that the profit level would need to fall by €20 per unit. Analyse the implications of these observations, and find the most profitable solution in the light of them. (c) The manager is disappointed that product 2 is not in the suggested mix. Explore the effect of producing 2000 units of product 2 on the current solution. (d) A fifth product, requiring 30 man-machine hours per 100 units at each of stages A and B, offers a profit per unit of €25. What now is the optimal product mix?
- (a) (i)Explain the terms balanced transportation problem and dummy source. (ii) Why are there m+n-1 basic variables in a basic feasible solution to a balanced m by n transportation problem? (b) The table gives a firm’s production capacity and orders for a special product. Costs are €30 per unit on regular time, €40 per unit on overtime and €3 per unit per month for inventory. Inventory costs are incurred on goods which are not sold in the month in which they are produced.
Month Production Capacities Orders August Regular time 300, overtime 100 _ September Regular time 300, overtime 100 500 October Regular time 200, overtime 100 200 November Regular time 200, overtime 100 600
(ii) Sketch net present value versus discount rate for devices A and B on a single graph by plotting NPV at 0, 10, 12, and 15%. (iii) For what range of discount rates would device A be preferred to device B? (b) (i) Explain the term internal rate of return (IRR). (ii) A project is expected to have the following costs and benefits, in thousands of euro.
Year Investment Benefit 0 4000 1 1200 2 1410 3 1875 4 1150
Determine the internal rate of return here. (c) If projects are ranked according to the NPV criterion, and also according to the IRR criterion, will the rankings necessarily agree? Justify your answer.
- The treasurer of Dse4 plc is faced with a decision as to how best to invest €1,000,000 in
funds for the next year. The treasurer has identified the investment options shown below. The total return received from each is dependent on general economic and financial conditions for the year, as shown in the table. The table also shows the probabilities associated with the possible states of the economy.
Anticipated total return, %
Investment options Economy rises Economy stabilises Economy declines
Bonds 7 9 12
Commercial paper 8 10 14
Stocks 25 6 2
Probability 0.1 0.2 0.
(i) Calculate the expected monetary value for each investment option, and hence identify the optimal option according to the expected monetary value criterion
(ii) Produce the associated opportunity loss table and determine the best action according
to the expected opportunity loss criterion. What is the expected value of perfect
information here?
(iii) An investment consultant has approached Dse4’s treasurer with an offer to provide
help in forecasting economic conditions. She offers the service for €5000, and shows the
following ‘track record’ of her company’s accuracy over the past 40 years:
Actual economy
Predicted economy Increased Stabilised Declined
Economic increase 7 3 2
Economic stability 3 14 2
Economic decline 1 3 5
Construct a decision tree to represent the problem of whether or not the consultant should
be hired. If the consultant predicts an economic increase, what is the expected monetary
value of the stocks option?
Note that it is not necessary to fill in all the values on the decision tree.
